Compressed sensing, which draws on information theory, probability theory, and other fields, has generated a great deal of excitement with its nontraditional approach to signal processing.
Compressed sensing emerged initially from an experiment inspired by a real-world problem with magnetic resonance imaging (MRI). The goal of the experiment, headed by Charles Mistretta at the University of Wisconsin, Madison, was to speed up the notoriously slow MRI process to make it more comfortable for patients, compensate for their minor movements, increase MRI throughput, and possibly even make the process fast enough to conduct 3D imaging. Because
MRI hardware relies on a quantum effect to determine the density of protons in a patient’s body, the data-capture process cannot be shortened by improving the hardware’s core technology. Therefore, the question initially posed by the researchers working on the problem is whether the time it takes to perform an MRI can be reduced by capturing fewer samples and reconstructing a full image from only a small fraction of the traditional amount of required data. While conventional sampling theory suggests doing so would not be possible, the University of Wisconsin researchers applied standard image-reconstruction algorithms on heavily subsampled MRI data. But the results were inadequate, so the researchers turned to Emmanuel Candes, a professor of applied and computational mathematics at the California Institute of Technology, for as-
For many years, traditional signal processing has relied on the Shannon-Nyquist theory, which states that the number of samples required to capture a signal must be determined by the signal’s bandwidth. An alternative sampling theory, called compressed sensing or compressive sampling, turns the Shannon-Nyquist theory on its head. The idea behind compressed sensing is to accurately acquire signals from relatively few samples. The theory was so revolutionary when it was created a few years ago that an early paper outlining it was initially rejected on the basis that its claims appeared impossible to substantiate.
Today, however, compressed sensing is attracting a great deal of interest from mathematicians, computer scientists, and both optical and electrical engineers. And the theory is inspiring a new wave of lab work to produce systems that require far less power and operate more efficiently than those that rely on the traditional capture-compress paradigm. These systems include applications for
industrial imaging, digital photography, biomedical imaging, and other forms of analog-to-digital conversion.
the left mRi image suffers from blurred edges, numerous artifacts, and low resolution. the phantom image on the right was produced with minimally sampled fourier coefficients using 5% of the original mRi data, and is the same as the original mRi phantom (not shown here).
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